There are many different functional forms of
the accumulation function, a(t)
However, there are two functions that are
used most often in the financial world
These two functions represent two different
types of interest calculation:
1. Simple Interest (se
Chapter 1 The Time Value of Money
In any financial transaction, there are two
parties:
The lender and the borrower
Consider the following transaction:
Person A lends money to person B
person A is called the lender or
investor
person B is called the borr
Poor Health Medical Needs MODULE 3
If an individual gets sick or needs medical treatment, he/she will need to obtain:
1
Hospitalization (includes surgical operations), or
2
Treatment from a medical practitioner (e.g. physician), or
3
Drugs, or
4
Other med
(III) Government Plans (MODULE 2)
Canada Pension Plan (CPP)
Introduction
The CPP came into effect Jan. 1/66
Quebec opted out of the Federal plan and created the QPP similar to CPP
CPP is compulsory
covers practically all employed people (including the
Group RRSPs (MODULE 2)
These have gained in popularity over the years as an alternative to pension plans
Main reason is that they are not subject to pension standards legislation
Advantages of Group RRSPs (When compared to RPPs)
No plan text to be registe
Ontario Retirement Pension Plan (ORPP)
Rationale (Why?)
Studies have shown that people are not saving
enough for retirement
Many workers do not have a pension plan
through their employer
Plus, many people change jobs/employers
throughout their careers
The Problem of Old Age (MODULE 2)
Long Term Care
Most elderly people require no assistance with their activities of daily living
however, a substantial proportion of the elderly will require care at some point
one study stated 40% of elderly will require
Longer Absences from Ontario
Will OHIP cover me during a longer absence? In some circumstances (described below), your
eligibility for Ontario health insurance coverage (OHIP) may continue while you are absent from
Ontario for more than 212 days in a 12-m
Chapter 3 Simple Annuities
Introduction
Suppose you deposit $500 every 6-months
for 2-years.
How much will you have accumulated
immediately after the 4th deposit if j2 = 6%?
Draw a timeline
Deposit 500 every 6 months for 2 years, for 4 total
periods
I=0.0
Discounted Value of An Ordinary Simple
Annuity (section 3.3)
Consider the following
An ordinary simple annuity consisting of
n-payments of $1
we wish to determine the present value, A,
of these payments at the beginning of the
term
that is, what is the
Compound Interest at Changing Interest
Rates (section 2.7)
In all examples/exercises so far, the interest
rate was assumed to be constant throughout
the term of the investment
frequently, however, the interest rate
changes over the term of a loan or
inve
Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are two
parties:
The lender and the borrower
Consider the following transaction:
Person A lends money to person B
person A is called the lender or
in
Compound Interest at Changing Interest
Rates (section 2.7)
In all examples/exercises so far, the interest
rate was assumed to be constant throughout
the term of the investment
frequently, however, the interest rate
changes over the term of a loan or
inve
Chapter 2 Compound Interest
Fundamental Compound Interest Formula
(scection 2.1)
Compound Interest
The interest earned in any given period of
time is added to the principal and it
thereafter earns interest
the interest is said to be compounded
Definition
Determining the Rate and Time (2.5)
(I)
Determining the Rate
Given: P, S, n
Determine: i
Start with: S = P(1 + i )n
(1+ i )n = S/P
(1+ i ) = (S/P)1/n
i = (S/P)1/n 1
most of the time you are asked to solve for
jm=i
Example 2.5.1
A) At what nominal rate
Partial Payments (section 1.4)
When a person borrows money, they can
pay back the loan, with interest, in one of
two ways:
1. With a single payment on the due date
2. With a series of partial payments
during the whole term of the loan
It then becomes nec
Determining the Rate and Time (2.5)
(I)
Determining the Rate
Given: P, S, n
Determine: i
Start with: S = P(1 + i )n
(1+ i )n = S/P
(1+ i ) = (S/P)1/n
i = (S/P)1/n 1
most of the time you are asked to solve for
jm=i
Example 2.5.1
A) At what nominal rate j2
Annuities Where Payments Vary
(section 4.4)
Not all annuities have a level series of
payments; instead we are going to look
at annuities where the payments change
every period
Two Standard Types
(I)
Payments vary in terms of a
constant ratio
these are an
Chapter 4 General and Other Annuities
General Annuities (section 4.1)
General annuities are annuities (either
ordinary or due) where the interest
period and the payment period are NOT
the same
we will look at annuities where
payments are made more/less
f
Perpetuities (section 4.3)
A perpetuity is an annuity where the
payments begin on a fixed date and
continue forever
since payments continue forever, it is
meaningless to calculate accumulated
values
we will only look at the present value
of perpetuities
Determining the Term of an Annuity
(section 3.5)
Given: S or A, R, i
Determine: n
Method
You can use logs to solve:
S = R sn|i
or
A = R an|i
Problem
n will rarely be an integer
will need to calculate a final payment
that is different from R in order to
Discounted Value of An Ordinary
Simple Annuity (section 3.3)
Consider the following
An ordinary simple annuity consisting of
n-payments of $1
we wish to determine the present value,
A, of these payments at the beginning
of the term
that is, what is the
Example 2.4.4
A loan is taken out on October 4, 2010 and is
due on May 11, 2013 at j4 = 6%. Calculate the
maturity value of the loan using both the exact
and practical methods.
Solution to 2.4.4
Determining the Rate and Time (2.5)
(I)
Determining the Rate
Chapter 2 Compound Interest
Fundamental Compound Interest
Formula (section 2.1)
Compound Interest
The interest earned in any given period
of time is added to the principal and it
thereafter earns interest
the interest is said to be compounded
Definition
Chapter 1 Simple Interest and Discount
Simple Interest (section 1.1)
In any financial transaction, there are
two parties:
The lender and the borrower
Consider the following transaction:
Person A lends money to person B
person A is called the lender or
in
Compound Interest at Changing Interest
Rates (section 2.7)
In all examples/exercises so far, the
interest rate was assumed to be constant
throughout the term of the investment
frequently, however, the interest rate
changes over the term of a loan or
inve
Chapter 3 Simple Annuities
Introduction
Suppose you deposit $500 every 6months for 2-years.
How much will you have accumulated
immediately after the 4th deposit if
j2 = 6%?
Suppose you made semi-annual deposits for
40-years? (80 payments in total) What is
Partial Payments (section 1.4)
When a person borrows money, they can
pay back the loan, with interest, in one of
two ways:
1. With a single payment on the due date
2. With a series of partial payments
during the whole term of the loan
Methods to Handle Pa
Designing a STD or LTD Plan
Fundamental issues include:
1.
Definition of Disability
most plans use own occ for the STD period plus first 2 years of the LTD
claim
any occ is used thereafter
Some LTD plans quantify the test as follows:
2.
ee is considered d
(III) Employer Disability Income Plans
Most employers provide ees with some level
of disability income replacement coverage
in the event of absence from work because
of:
illness, or
accident
whether or not the cause is related to
work
We will split er